All open-source licenses allow reskinning and modifying the game. If they didn't, it would be totally against the spirit of open source. However, some have provisions that require that credit be given to you for the original version.
The Mozilla Public License requires acknowledgment of the original version of the game as well as a list of changes; that might fit your needs. The Open Source Definition (which is what is being used to judge whether a license is open source) allows licenses that require modified versions of your game to use a new name, but I'm not sure if there are any licenses out there that actually have such a requirement.
You could take an existing license and modify it to fit your needs as long as it meets all the requirements of the Open Source Definition. This means that you have to allow modification of your game under the same license you use, even if it is under a different name from the original.
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